code: def _autograd_is_indep_analytic(func, *args, **kwargs):
      """Test analytically whether a function is independent of its arguments
      using Autograd.
  
      Args:
          func (callable): Function to test for independence
          args (tuple): Arguments for the function with respect to which
              to test for independence
          kwargs (dict): Keyword arguments for the function at which
              (but not with respect to which) to test for independence
  
      Returns:
          bool: Whether the function seems to not depend on it ``args``
          analytically. That is, an output of ``True`` means that the
          ``args`` do *not* feed into the output.
  
      In Autograd, we test this by sending a ``Box`` through the function and
      testing whether the output is again a ``Box`` and on the same trace as
      the input ``Box``. This means that we can trace actual *independence*
      of the output from the input, not only whether the passed function is
      constant.
      The code is adapted from
      `autograd.tracer.py::trace
      <https://github.com/HIPS/autograd/blob/master/autograd/tracer.py#L7>`__.
      """
      # pylint: disable=protected-access
      node = VJPNode.new_root()
      with trace_stack.new_trace() as t:
          start_box = new_box(args, t, node)
          end_box = func(*start_box, **kwargs)
  
      if type(end_box) in [tuple, list]:
          if any(
              isbox(_end) and _end._trace == start_box._trace
              for _end in end_box
          ):
              return False
      elif isinstance(end_box, np.ndarray):
          if end_box.ndim == 0:
              end_box = [end_box.item()]
          if any(
              isbox(_end) and _end._trace == start_box._trace
              for _end in end_box
          ):
              return False
      else:
          if isbox(end_box) and end_box._trace == start_box._trace:
              return False
      return True
  
file_path: pennylane/pennylane/math/is_independent.py
imports: import warnings
  import numpy
  from autograd.tracer import isbox, new_box, trace_stack
  from autograd.core import VJPNode
  from pennylane import numpy
label_desc: Use image node_id 1 for calling a global function with example usage: _autograd_is_indep_analytic(func) and returns: True, False, False, False